CCHHAAPPTTEERR 66PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 893 50 mmss50 mm50 mm100 mm PROBLEM 6.1 Three full-size 50  100-mm boards are nailed together to form a beam that is subjected to a vertical shear of 1500 N. Knowing that the allowable shearing force in each nail is 400 N, determine the largest longitudinal spacing s that can be used between each pair of nails. SOLUTION 336411(100)(150) 28.125 10 mm12 12 Ibh 6428.125 10 m 2(100)(50) 5000 mmA 150 mmy 33 631250 10 mm 250 10 m QAy 636(1500)(250 10 )13.3333 10 N/m28.125 10  VQqI nail2qs F 3nail32(2)(400)60.0 10m13.3333 10 Fsq 60.0 mms PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 894 50 mmss50 mm50 mm100 mm PROBLEM 6.2 For the built-up beam of Prob. 6.1, determine the allowable shear if the spacing between each pair of nails is s  45 mm. PROBLEM 6.1 Three full-size 50  100-mm boards are nailed together to form a beam that is subjected to a vertical shear of 1500 N. Knowing that the allowable shearing force in each nail is 400 N, determine the largest longitudinal spacing s that can be used between each pair of nails. SOLUTION 336411(100)(150) 28.125 10 mm12 12 Ibh 6428.125 10 m 2(100)(50) 5000 mmA 150 mmy 33 631250 10 mm 250 10 m QAy VQqInail2qs F Eliminating ,q nail2VQ FIs Solving for V, 63nail632 (2)(28.125 10 )(400)2.00 10 N(250 10 )(45 10 ) IFVQs 2.00 kNV ◄PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 895 2 in.2 in.6 in.sss2 in.4 in. PROBLEM 6.3 Three boards, each 2 in. thick, are nailed together to form a beam that is subjected to a vertical shear. Knowing that the allowable shearing force in each nail is 150 lb, determine the allowable shear if the spacing s between the nails is 3 in. SOLUTION 32132433 4243141231121(6)(2) (6)(2)(3) 112 in1211(2)(4) 10.6667 in12 12112 in234.67 inIbhAdIbhIIIII I  311nail(6)(2)(3) 36 in(1)(2)QAyqs FVQqI Dividing Eq. (2) by Eq. (1), nail1 VQsFI nail(150)(234.67)(36)(3)FIVQs 326 lbV PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 896 sss120 mm80 mm20 mm20 mm PROBLEM 6.4 A square box beam is made of two 20 80-mm planks and two 20 120-mm planks nailed together as shown. Knowing that the spacing between the nails is 30s mm and that the vertical shear in the beam is 1200 N,V determine (a) the shearing force in each nail, (b) the maximum shearing stress in the beam. SOLUTION 3322 1133 64641112 1211(120)(120) (80)(80) 13.8667 10 mm12 1213.8667 10 mIbh bh (a) 21133 63111(120)(20) 2400 mm50 mm120 10 mm 120 10 mAyQAy  636nail(1200)(120 10 )10.3846 10 N/m13.8667 102  VQqIqs F 33nail(10.3846 10 )(30 10 )22qsF nail155.8 NF   (b) 133 3363(2)(20)(40)(20)12010 3210 15210mm152 10 mQQ 6max63(1200)(152 10 )(13.8667 10 )(2 20 10 )VQIt 3329 10 Pa max329 kPa PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 897 16 ⫻ 200 mmS310 ⫻ 52 PROBLEM 6.5 The American Standard rolled-steel beam shown has been reinforced by attaching to it two 16 200-mm plates, using 18-mm-diameter bolts spaced longitudinally every 120 mm. Knowing that the average allowable shearing stress in the bolts is 90 MPa, determine the largest permissible vertical shearing force. SOLUTION Calculate moment of inertia: 2 264 64**(mm)(mm) (10mm) (10 mm)PartTop plate 3200 82.43 0.07160.5S310 52 6650 0 95.3Bot. plate 3200 82.43 0.07160.5164.86 95.44dAAdI 2646433 63plate plate23262bolt bolt663bolt all bolt*305 16160.5 mm22260.3 10 mm 260.3 10 m(3200)(160.5) 513.6 10 mm 513.6 10 m(18 10 ) 254.47 10 m44(90 10 )(254.47 10 ) 22.90 10 NdIAd IQAdAdFAqs     33boltbolt363362 (2)(22.90 10 )2381.710N/m120 10(260.3 10 )(381.7 10 )193.5 10 N513.6 10FFqsVQ IqqVIQ   193.5 kNV PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 898 C12 ⫻ 20.716 in. ⫻ in.Czy12 PROBLEM 6.6 The beam shown is fabricated by connecting two channel shapes and two plates, using bolts of 34-in. diameter spaced longitudinally every 7.5 in. Determine the average shearing stress in the bolts caused by a shearing force of 25 kips parallel to the y axis. SOLUTION 4C12 20.7: 12.00 in., 129 inxdI  For top plate, 32412.00 1 16.25 in.22211 1(16) (16) (6.25) 312.667 in12 2 2tyI      For bottom plate, 4312.667 inbI  Moment of inertia of fabricated beam: 43plate platebolt222bolt